At Omega service centres, they fully polish everything first before brushing. For me it depends on the level of damage if I polish first as its not always needed if the wear is light.
It's not really necessary to do any of this by hand, but for someone who has no or little experience it's much safer than using machinery. If you know what equipment and techniques to use, sharp edges can be maintained when using a buffing machine, but the skill and experience has to be there, and based on the cases I see, many people lack these skills.
The absolute biggest mistake made is that people try to remove all the scratches and dents. The biggest judgement call is knowing when to stop...
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